That’s because they’re difficult to spot. Even buying a model known for reliability is no guarantee that it won’t have problems. That’s what Deborah Boulet of Canterbury, Conn., found when she bought a used 2011 Mazda3 and discovered water leaking into its trunk on the day she took delivery. Upon further investigation, her attorney found that the car had been hit by a snowplow and shoddily repaired. Now towels soak up the water as Boulet fights a legal battle to get the dealership to buy back her car. “I don’t trust this car at all anymore, and I drive it as little as possible,” she said. “It’s been a nightmare.”

According to Carfax, a service that provides vehicle history ­reports, about 20 percent of cars on the road have some sort of accident damage.

But a 2009 Consumer Reports investigation showed that reports from Carfax and its main competitor, AutoCheck, can’t catch everything. Differing state laws governing salvage titles allow for loopholes big enough to drive a rebuilt wreck through. Often, even when a car’s title is conspicuously labeled as salvaged, consumers such as Boulet never see it. Ask to see the title before you buy a used car, and be especially wary of any car with a “lost” title.